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3 years ago

Only the function represented by graph has an inverse function.

Mathematics

1 answer:

Arlecino [84]3 years ago

4 0

Answer:

Only the function represented by graph 2 has an inverse function

Step-by-step explanation:

* Lets explain the inverse of the function

- The Function is a relation between x-coordinates and the y-

coordinates of the order pairs under the condition every

x-coordinate has only one y-coordinate

- Ex: R = {(2 , 3) , (1 , 5) , (-2 , -3)} is a function because every x-

coordinate has only one y-coordinate and R = {(2 , 3) , (-1 , 4) ,

(2 , 5)} not a function because the x-coordinate 2 has two y-

coordinates 3 and 5

- We use the vertical line to test the graph is function or not, if

the vertical line intersects the graph in one point then the

graph is function if intersects it in more than one point then the

graph is not function

- We have two types of function one-to-one function and

many-to-one function

# one-to-one function means every x-coordinate has only 1 y-coordinate

# many-to-one function means some x-coordinates have only 1

y-coordinate

- We find the inverse function by switching x and y, then one-to-

one function has inverse but many-to-one has not inverse

because when we switched x and y it will be one-to-many

means one x-coordinate has many y-coordinates and this is not

a function

- We use the horizontal line to test the graph of the function has

inverse or not, if the horizontal line intersects the graph in one

point then the function of the graph has inverse if it intersects

the graph in more than one point ,then the function of the

graph has no inverse

* Now lets test all the graphs by using the horizontal line

# graph 1

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 1 has no inverse

# graph 2

∵ The horizontal line cuts the graph in just 1 point

∴ The function of graph 2 has inverse

# graph 3

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 3 has no inverse

# graph 4

∵ The horizontal line cuts the graph in more than 1 point

∴ The function of graph 4 has no inverse

* Only the function represented by graph 2 has an inverse function

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3 years ago

Find the probability that a randomly generated bit string of length 10 does not contain a 0 if bits are independent and if:a) a

lara31 [8.8K]

Answer:

A) 0.0009765625

B) 0.0060466176

C) 2.7756 x 10^(-17)

Step-by-step explanation:

A) This problem follows a binomial distribution. The number of successes among a fixed number of trials is; n = 10

If a 0 bit and 1 bit are equally likely, then the probability to select in 1 bit is; p = 1/2 = 0.5

Now the definition of binomial probability is given by;

P(K = x) = C(n, k)•p^(k)•(1 - p)^(n - k)

Now, we want the definition of this probability at k = 10.

Thus;

P(x = 10) = C(10,10)•0.5^(10)•(1 - 0.5)^(10 - 10)

P(x = 10) = 0.0009765625

B) here we are given that p = 0.6 while n remains 10 and k = 10

Thus;

P(x = 10) = C(10,10)•0.6^(10)•(1 - 0.6)^(10 - 10)

P(x=10) = 0.0060466176

C) we are given that;

P((x_i) = 1) = 1/(2^(i))

Where i = 1,2,3.....,n

Now, the probability for the different bits is independent, so we can use multiplication rule for independent events which gives;

P(x = 10) = P((x_1) = 1)•P((x_2) = 1)•P((x_3) = 1)••P((x_4) = 1)•P((x_5) = 1)•P((x_6) = 1)•P((x_7) = 1)•P((x_8) = 1)•P((x_9) = 1)•P((x_10) = 1)

This gives;

P(x = 10) = [1/(2^(1))]•[1/(2^(2))]•[1/(2^(3))]•[1/(2^(4))]....•[1/(2^(10))]

This gives;

P(x = 10) = [1/(2^(55))]

P(x = 10) = 2.7756 x 10^(-17)

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3 years ago

Your jewelry business orders $1320 in supplies each month. In each month, you can usually sell an earring/ring set for about $55

steposvetlana [31]

Answer:

Given,

The jewelry business orders $ 1320 in supplies each month.

That is, the invested amount = $ 1320,

Also, the selling price of each earring/ring set = $ 55,

Part 1 : Let x be the number of set that have been sold each month to break even ( in which revenue and invested amount are equal )

So, Total revenue ( the cost of x sets) = 55x,

⇒ 55x = 1320

Divide both sides by 55,

We get,

x = 24

Hence, 24 sets are needed to sell each month to break even.

Part 2 : Let y be the number of sets in which the profit is $ 715,

Total revenue = 55x

Profit = Total revenue - invested amount

⇒ 55x - 1320 = 715,

⇒ 55x = 715 + 1320

⇒ 55x = 2035

⇒ x = 37

Hence, 37 sets are sold for the total profit of $715.

Part 3 :

Revenue in selling 7 sets = 55 × 7 = $ 385

Profit = $ 385 - $ 1320 = - $ 935

Hence, the profit is - $ 935 after selling 7 sets.

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Step-by-step explanation:

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Answer:

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